Let $R$ be a reflexive relation on a set $A$ and $I$ be the identity relation on $A$. Then

Let $R$ be a relation on $\mathbb{Z} \times \mathbb{Z}$ defined by $(a, b) R (c, d)$ if and only if $ad - bc$ is divisible by $5$. Then $R$ is

Show that the relation $R$ in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3), (1, 2), (2, 3)\}$ is reflexive but neither symmetric nor transitive.

Let $R$ be a relation on the set $N$ of natural numbers defined by $nRm \iff n$ is a factor of $m$ (i.e.,$n|m$). Then $R$ is

Let the relation $R_1$ be defined by $R_1 = \{ (a, b) | a \ge b, a, b \in R \}$. Then $R_1$ is:

Let $R$ be the relation in the set $\{1, 2, 3\}$ given by $R = \{(1, 1), (2, 2), (3, 3)\}$. Choose the correct answer.